"Don't link to other sites or you'll improve their ranking. Link to mine instead" is pretty much what this site is saying.
This is why Google created rel="nofollow"[1] and if you are really worried about where you pass PageRank to it is a much better alternative than linking to some random 3rd party site while passing value back to them.
Since the Panda update everybody should be using rel="nofollow" on all outbound links, otherwise you risk getting knocked back to page 100 should any of the sites you ever link to trip a flag that leads google to classify them as a spammer.
For what it's worth, there are many indications that using more than a few no-follow links on your website 1) hurts your SEO standing, and 2) still passes Link Juice to the external website (just slightly less than its do-follow counterpart).
This happened after Google discovered that people were abusing no-follow - by trying to hoard the website's weight and not sharing it with anybody.
You should definitely not rel="nofollow" all outbound links. Do it to sites that have a risk of becoming a spam site maybe, but a quality site usually doesn't become a spam site overnight and you'll do more harm than good to yourself adding by rel="nofollow" to every single outbound link. Google wants you to link out to quality sites so you don't need to nofollow those.
Fails to parse http://io/ as valid URL. Same with IDNs, http://пример.испытание/. Okay, that's obscure cases, but when you're writing yet another link shortener you really should know quite a bit about URIs (and IRIs).
tinyurl and other shorteners generally use a 301 redirect, which often does pass 'link juice'.
nofollow is usually under the control of the webmaster. Which may or may not be the same as the content creator.
Think forums and blog comments, as poster you generally have no control if nofollow is added to links. Usually it should be, but no garentee.
Also think of sites like twitter, facebook and g+, again you can't ensure that nofollow is added. Similally when that content is then copied or syndicated. You can usually hope that the copier will perserve the link itself, but they may or may not choose to 'nofollow' the copied link.
And lastly, 'bad' bots, may well ignore the nofollow anyway. It would have to be broken/clever bot to get the destiniation from donotlink
If you refer to the "how" page, you'll see that they use noindex and nofollow, a robots.txt to discourage crawling, and a blank 403 to any crawler ignoring the robot.txt
Hacked? More than likely they just drop the service in 10 months because they are a fly by night operation that lacks any plan? Then their domain gets picked up by a content farm.
I prefer to let the search engines worry whether a link is supposed to pass link juice or not. I've already given Google my fair share of information these days anyway.
Google isn't worried about your site. They will drop your ranking if they think that is for the greater good. If you are going to link without nofollow then you are trusting every site you link to never do anything that even vaguely looks spammy or like paid linking. If you link to a site that pays for some links (according to google's spam algos) then you will get 'panda slapped' and recovering from that is very hard.
This is why Google created rel="nofollow"[1] and if you are really worried about where you pass PageRank to it is a much better alternative than linking to some random 3rd party site while passing value back to them.
[1]https://support.google.com/webmasters/answer/96569?hl=en